The DRC government yesterday (Monday) invited a new inquiry by UN investigator Roberto Garreton into alleged human rights abuses. Human Rights minister Leonard Okitundu said President Laurent-Desire Kabila was prepared to welcome back Garreton, who was denied access to the DRC in 1997 after authoring a report on alleged massacres of Rwandan Hutu refugees by Kabila's then rebel forces.
An allied air raid on Kisangani on Sunday killed 17 people including five children, rebel leader Ernest Wamba dia Wamba told the Associated Press today (Tuesday). Reuters quoted aid workers in the rebel-held town as saying 40 people died in the bombing by an Antonov aircraft. Mouvement de liberation congolais (MLC) rebel leader Jean-Pierre Bemba told the BBC today from Kisangani that the aircraft was Sudanese.
The DRC government said on Sunday the towns of Gemena and Libenge had been recaptured. A military communique said 117 rebels were killed at Gemena, and Ugandan and Rwandan soldiers were taken prisoner. It added that Bemba narrowly escaped capture, and rebels fleeing to Zongo were ambushed. Reuters quoted sources across the border in the Central African Republic as saying Libenge had been bombed by allied forces. AFP reported from Bangui yesterday that mortar fire and heavy shooting was heard in the Zongo area, but could not confirm who was doing the shooting.
DRC state TV said yesterday Kabila was to attend this weekend's Lusaka summit on the Congo conflict. However, AP reported Wamba dia Wamba as insisting today that the rebel Rassemblement congolais pour la democratie (RCD) would not be at the meeting unless they were assured of face-to-face negotiations with Kabila. Regional mediator, Zambian President Frederick Chiluba, said on Sunday that 12 countries are due to attend the summit.
The South African newspaper 'Business Day' reported yesterday a government source as saying Chiluba postponed a meeting on Sunday with Deputy President Thabo Mbeki because he had failed to win agreement from Zimbabwe and DRC over rebel participation at the summit. The postponement "is a signal that the stalemate continues," the source said.
A Zimbabwean military transport plane crashed on the outskirts of Kinshasa killing all five people on board, the DRC ministry of defence said yesterday. The statement, reported by SAPA news agency, said the Spanish-built Casa aircraft crashed because of technical problems and bad weather conditions.
A two-day high-level meeting on Burundi began yesterday at the UN headquarters in New York. UN spokesman Fred Eckhard said participants were expected to discuss resource requirements for the current Arusha negotiation process and peace building activities for the country. Former Tanzanian President Julius Nyerere was among the senior regional, donor and UN officials attending the meeting. Diplomatic sources said the meeting was likely to agree to continued financing for the Arusha peace process until August this year.
Regional leaders are due to meet in Arusha, Tanzania on 23 January to discuss the Burundi situation. Humanitarian sources told IRIN Nyerere had been under considerable pressure to end sanctions against Bujumbura and a compromise now looked likely where they would be suspended, but not cancelled.
Lord's Resistance Army (LRA) rebels abducted 80 people yesterday in northern Uganda, the independent 'Monitor' newspaper reported today. The raid took place in Aswa county, five km north of Gulu town. The state-owned 'New Vision' reported fierce fighting yesterday at Lacor, 12 km west of Gulu. The paper said that soldiers had been wounded in the clash. In separate incidents on Friday and Saturday around Gulu, the newspaper reported that three rebels were killed and an LRA commander and six other rebels surrendered.
American and British diplomatic missions in Kampala were shut for a second day today. No offical reason was given for the closures, but news reports said it was on security grounds.
Britain is trying to restore diplomatic relations with Khartoum damaged last year by the US bombing of a pharmaceutical factory, a foreign office minister said yesterday. "We have been in contact with the Sudanese to see if we can remedy the situation," Baroness Liz Symons said in a written answer to a parliamentary question, news organisations reported.
A political organisation representing Nuba people has applied for registration as a political party, Reuters reported yesterday. The Sudanese National Party of veteran Nuba politician Reverend Philip Gabboush on Sunday became the 11th political association to register, the dispatch said. However, apart from a splinter group of the Democratic Unionist Party, Sudan's main opposition groups have boycotted the process.
Reuters reported today the Eritrean government as saying it had received intelligence reports that Ethiopia was planning to launch fresh attacks in the border dispute between the two countries and called for a ban on all hostilities. The foreign ministry was quoted as saying in a statement that Western intelligence sources and others had reported the Ethiopian government would launch attacks against Eritrea between mid-January and mid-February from three directions. The latest accusation takes place at the same time as a renewed US attempt to broker a solution to the border dispute between the Horn of Africa nations, led by US envoy Anthony Lake.


text:
\section{Introduction}
Double-stranded DNA (dsDNA) is a linear semiflexible polymer chain with persistence lengths of about 150 base pairs (bp) ($50$ nm) and cross-section diameter of about $2$ nm. In aqueous solutions DNA molecules are highly negatively charged due to dissociated phosphate groups along the chain backbone that confer to B-form ds-DNA a bare base-pair charge of $2 e_0$ per 0.34 nm length of DNA, engendering strong repulsive interactions along and between DNA molecules \cite{RP1}. Nevertheless, under specific solution conditions DNA molecules can be induced to condense into highly compact structures that phase separate from the solution \cite{DNAcond}. In these condensates DNA is in a liquid crystalline state \cite{Maniatis,Evdokhimov} with lattice spacings close to measured spacings in bulk DNA liquid crystals at the same solution conditions \cite{Rau84,Podgornik94,Strey99}. The phenomenon of semiflexible polymer condensation is not specific to DNA only but can be observed in other semiflexible polyelectrolytes as well, e.g. F-actin filaments \cite{Tang}. The morphology of these condensates varies depending on the method of preparation \cite{Hud05} as well as on the dynamics of the nucleation and growth of the condensate \cite{Vilfan06,Muthukumar2005}. In what follows we will make the simplifying assumption that the condensate morphology is an equilibrium property, eventually reached after different nucleation and growth relaxation processes are over, and study the consequences.

Previous attempts at a theoretical analysis of DNA condensation in the presence of various condensing agents shed light on the resulting ordered nematic DNA structure often in the form of toroidal and/or rodlike globules \cite{Gros_khok}. Different aspects of this collapse transition have been scrutinized in order to deduce the detailed geometry of the aggregate and the corresponding phase diagram \cite{history} as well as their dependence on the assumed form of the elastic energy and the DNA-DNA or DNA-condensing agent interaction \cite{Interact}. In what follows we will revisit the problem of the stability and phase diagram of the various condensed structures of DNA in light of the recent understanding of the interactions driving the condensation transition in the case of polyvalent counterions and osmoticants, as well as the emerging details of the non-linear nature of the DNA elastic energy. The theoretical approach advocated  here, combined with Monte Carlo simulations, provides a simple and unified foundation on which the effects of various components of the DNA condensation phenomenon can be compared and assessed.

When condensed in a very dilute solution,  the most commonly observed DNA condensate morphologies are torus-like and rod-like (see Figs.\ref{fig:fig1} and \ref{fig:fig2}). A typical compact structure has the size of approximatively $100$ nm, with an inner hole about $30$ nm wide in the case of the toroidal aggregate. It is found to be relatively robust with respect to the length of the DNA involved in the condensation. The packing of DNA strands inside the condensed structure is highly ordered with a predominantly hexagonal packing in the plane perpendicular to the toroidal main axis \cite{Rawat09,Stukan06, Ishimoto08,Stukan03, Schnurr02, Starostin13}. The condensation can be induced by a variety of {\sl condensing agents}.
Among these flexible polymers, such as PEG (poly-ethylene-glycol), at large enough concentrations, the presence of salt (PSI-condensation = (P)olymer and (S)alt (I)nduced condensation) induces condensation of both DNA as well as F-actin filaments \cite{Interact,Renko}.

 The mechanism here appears to be osmotic depletion interactions \cite{Depletion} due to the exclusion of the polymer from the DNA subphase. More commonly exploited condensation agents in various biological settings are the multivalent counterions. In fact many, but not all, multivalent cations induce ds-DNA condensation. Those that do condense ds-DNA at finite concentrations are Mn$^{2+}$, Cd$^{2+}$, Co(NH$_3$)$^{3+}$, polyamines such as spermidine$^{3+}$, spermine$^{4+}$, polylysine$^{+}$ and all the higher valency (poly)counterions. That electrostatics plays an important role in DNA condensation is clear but it is just as clear that it can not be the only factor driving it \cite{Curop,Cherstvy2011,Teif}. Furthermore, a radical reformulation of the theory of electrostatic interactions is needed \cite{Rudi2010,Rudibook}, based on the concept of the "strong-coupling" electrostatics between the multivalent salt counterions and the charges on the DNA backbone, in order to understand the counterintuitive change in sign of interactions between nominally equally charged bodies \cite{Rudibook,Perspective}.

While electrostatics should play an important role in the DNA condensation mechanism, it cannot be the sole and sometimes not even the dominant factor affecting it. For instance $\mathrm{Co(NH_3)}^{3+}$ is more efficient in condensing DNA than spermidine$^{3+}$, both being trivalent counterions, and the best condensing agents appear to be those that bind into one of the DNA grooves \cite{DeRouchey10}. These well documented ion specific effects \cite{Rau92}  furthermore suggest that interaction of condensing ions with water molecules, i.e. hydration interactions, provide the necessary specificity that is absent in condensation interactions based exclusively on Coulomb interaction [for a recent review of hydration effects see Ref \onlinecite{Rau11}].

Apart from the polymer depletion and "strong-coupling" electrostatic interactions, a fundamental ingredient of any theory of semiflexible polymer condensation is their significant stiffness that frustrates the formation of a spherical globule \cite{Yamakawa,Svensek}. Without any stiffness effects, one would expect that the spherical globule would be the ground state of a flexible polymer by minimizing its surface energy \cite{Grosbergbook}. Indeed, the local structure of this condensed phase consists of straight chains with parallel nematic alignment to minimize the bending energy.
However, even within this simple picture, it is not clear why this particular structure is necessarily favored with respect to other structures – such as, for instance, a rod-like structure – having similar characteristics. Nor is the role of the concrete form of the elastic energy as well as the interactions between DNA molecules that induce the condensation well understood.

In this paper we will address these issues using simple analytical arguments supported by numerical simulations, and discuss under what conditions the toroidal condensate is favored with respect to a rod-like counterpart. We will include the bending energy, the surface energy and the detailed interaction energy between polymer molecules in our {\sl {\sl Ansatz}} for the free energy whose minimization will provide us with the  equilibrium configuration of the condensate.

The outline of the paper is as follows: we first present the model with the corresponding packing geometry, and the non-equilibrium curvature, surface and interaction free energies written for the dominant configurations of a toroid and a spherocylinder. We then proceed to the analytical minimization of the total free energy for the toroidal and rod-like aggregate that we compare with Monte-Carlo simulations. We finally explore the effect of various interaction models and generalize the elastic energy {\sl {\sl Ansatz}} to the case of an intrinsic threshold. We conclude with a commentary on previous works and with an assessment on the validity of our approach.

\section{Model}

We consider a semiflexible polymer of length $L$ formed by $N$ spherical beads of diameter $b$. The bond length between consecutive beads is also taken to be equal to $b$ for simplicity.  A conformation of the polymer is given by the positions of the beads $\{{\bf r}_i,i=1,2,\ldots N\}$. We furthermore assume that all the energies involved in condensate morphology are sufficiently large so that entropic terms can be neglected. Hence we expect a compact phase for which only curvature, surface and interaction energy terms are present.

\subsection{Packing geometry}

In our model the polymer chain fills the condensate interior and is locally hexagonally packed. Consider a tessellation of a plane perpendicular to the long axes of the polymer, having a Schl\"afli symbol \cite{Coxeter69} ${p,q}$. For hexagonal packing the Schl\"afli symbol is ${6,3}$. The hexagonal packing fraction \cite{Coxeter69}
\begin{eqnarray}
\label{sec1:eq1}
\eta &=& \frac{\pi}{p} \cot\left(\frac{\pi}{p}\right)
\end{eqnarray}
for the case of hexagonal close packing ($p=6$) is then given by
\begin{eqnarray}
\eta_{\text{hex}}&=& \frac{\pi}{6}\cot\left(\frac{\pi}{6}\right) = \frac{\pi}{2 \sqrt{3}} =0.9069...
\label{sec1:eq2}
\end{eqnarray}
If the packing of polymers inside the aggregate is still hexagonal but not at the highest close packing fraction $\eta_{\text{hex}}$, where the separation between the polymer chains is equal to $d$, then $d \ge b$ and the packing fraction is given by:
\begin{equation}
\label{sec1:eq3}
\eta = \eta_{\text{hex}} \left(\frac{b}{d}\right)^2 .
\end{equation}
The hexagonal packing symmetry is thus still preserved but at a lower packing fraction. This will be important when we introduce soft interactions between polymer segments.

\subsection{Curvature and surface energy}
\label{subsec:curvature}

Within the worm-like chain model \cite{Rubinstein03} the elastic bending free energy is given by
\begin{equation}
\label{sec2:eq1}
U = \kappa \sum_{i=2}^{N-1} (1-\cos \theta_i),
\end{equation}
where $\kappa$ is the (reduced) stiffness, $\theta_i$ is the angle between ${\bf r}_{i-1,i}$
and ${\bf r}_{i,i+1}$ with ${\bf r}_{ij}={\bf r}_j - {\bf r}_i$. The energies are assumed to be in units of thermal energy $k_B T$, so that both $U$ and $\kappa$ are dimensionless variables. Here $k_B$ is the Boltzmann constant, $T$ the absolute temperature, and  we denote as $l_p = \kappa b$ the persistence length of the chain. If $R_i$ is the radius of curvature at the bead $i$, i.e. the radius of the circle through
${\bf r}_{i-1}$, ${\bf r}_{i}$, and ${\bf r}_{i+1}$, it is easy to show that
\begin{equation}
\label{sec2:eq2}
1 - \cos \theta_i = \frac{b^2}{2 R^2_i} \ .
\end{equation}

Assume that the chain forms a toroid of the mean radius $R$ and radius of the cross-section
$\Delta=\alpha R$ with $0 < \alpha < 1$ (see Fig. \ref{fig:fig1}). The limiting case $\alpha=0$ ($R \to \infty$) would correspond to a swollen conformation whereas $\alpha=1$ would correspond to a ``globular'' conformation with no inner hole inside the torus (not a sphere).

In the simplest case, one can furthermore  assume that the chain has a constant radius of curvature equal to $R$.
The bending energy in Eq. (\ref{sec2:eq1}) in the large $N$ limit
then simplifies to
\begin{equation}
U_{toroid} = \frac{\kappa}{2} \frac{Lb}{R^2} \ ,
\label{eq:etor1}
\end{equation}
where $L=Nb$.
Note that our constant radius of curvature approximation follows
the model proposed in Ref. \onlinecite{Hud95}
which claimed to predict a correct toroid size distribution. This
approximation may not be fully consistent with our previous assumption
on the hexagonal packing. Thus, we assume that the latter is not rigorously
valid but only essentially correct. An alternative model of DNA organization
inside the condensates based on perfect hexagonal packing \cite{Starostin06}  yields similar expression for bending
energy but only in the limit of thin condensate.
\begin{figure}[htbp]
\begin{center}
   \includegraphics[width=2.0in,angle=270]{Fig1.pdf}
\end{center}
\caption{(Left) Sketch of the DNA condensate as a toroidal phase. The mean
radius of the toroid is $R$. The radius of cross section is $\Delta = \alpha R$
with $0<\alpha<1$. (Right) The hexagonal packing within the cross section of
the torus.}
\label{fig:fig1}
\end{figure}
We assume (see Fig.\ref{fig:fig1} (b)) that the polymer tightly wraps around
the torus with $n_{loops}$ loops that are related to the two-dimensional
(cross-section) packing fraction $\eta$ given in Eq.
(\ref{sec1:eq2}) by the ratio of the occupied to the total surface
\begin{equation}
\label{sec2:eq3}
\eta = \frac{n_{loops} \pi (b/2)^2}{\pi (\alpha R)^2} .
\end{equation}
In order to compare low-energy configurations with different geometries, we need to translate the typical length scale of the problem ($R$ in this case) to the contour length $L$ of the polymer that is common to all configurations.   In the present case, we have
\begin{equation}
\label{sec2:eq5}
L= 2 \pi R n_{loops} = 8 \pi R  \eta \alpha^2 \left(\frac{R}{b} \right)^2
\end{equation}
Thus we end up with
\begin{equation}
\frac{R}{b} = \left(8 \pi \eta \alpha^2\right)^{-1/3} \left(\frac{L}{b} \right)^{1/3}
\label{eq:Rb}
\end{equation}
Inserting Eq. (\ref{eq:Rb}) into Eq. (\ref{eq:etor1}),  one obtains
\begin{equation}
U_{toroid} =  2\kappa \pi^{2/3} \eta^{2/3} \alpha^{4/3}
\left(\frac{L}{b}\right)^{1/3} .
\label{sec2:eq6}
\end{equation}

On the other hand, if we denote as $\sigma$ the surface tension, the surface energy of the toroid is, using Eq.(\ref{eq:Rb}) again,
\begin{eqnarray}
\sigma S_{toroid} &=& \sigma (2\pi\alpha R)(2\pi R) =
\nonumber \\
&=& \left(\sigma b^2\right) \pi^{4/3} \eta^{-2/3}\alpha^{-1/3}  \left(\frac{L}{b}\right)^{2/3}.
\label{eq:storoid}
\end{eqnarray}
Note that
\begin{equation}
U_{toroid} \sim \left(\frac{L}{b} \right)^{1/3} \qquad \sigma S_{toroid} \sim  \left(\frac{L}{b} \right)^{2/3}
\end{equation}
so the surface energy term is the dominant one for $L/b \gg 1$ unless the ratio $\kappa/\sigma b^2$ is very large.

Consider now the rod-like structure sketched in Fig. \ref{fig:fig2} as another
possible low energy conformation competing with the toroid. We assume a
spherocylindrical shape for the DNA condensate with circular cross-section of
radius $R$ and length $(\gamma + 2)R$ with $\gamma \ge 0$. The limiting case
$\gamma=0$ again corresponds to a ``globular'' conformation, albeit different
from the previous one. Within this compact structure the polymer chain folds in
such a way that parallel segments are hexagonally packed in the main body of
the structure and there are loops only at the two spherical caps (see
Fig.\ref{fig:fig2}).

\begin{figure}[htbp]
\begin{center}
   \includegraphics[width=3.0in,angle=270]{Fig2.pdf}
\end{center}
\caption{(Left) Sketch of the DNA condensate as a rod-like structure. (Right)
The hexagonal packing within the cross section of the rod}
\label{fig:fig2}
\end{figure}
As in the previous case, a relation between the length $L$ of the DNA polymer
and the characteristic geometry scale $R$ of the rod-like condensate can be
found hinging upon simple geometrical considerations. The total length $L$ of
the polymer is the sum of two parts: the straight part in the cylinder body
$L_{straight}$, and the loop part in the two spherical caps $L_{loops}$ that
can be estimated as
\begin{eqnarray}
\label{eq:eq19}
L_{straight} = \frac{4\eta \gamma R^3}{b^2}  &\qquad&
L_{loops}=\frac{16\eta R^3}{3b^2} \ .
\end{eqnarray}
In the above equations, the length is estimated as volume times the packing
fraction of the condensate divided by cross section area of the polymer.
Thus,
\begin{eqnarray}
\label{eq:eq21}
L &=& L_{straight} + L_{loops} = \frac{4\eta(\gamma+4/3)R^3}{b^2} \ .
\end{eqnarray}
Within the same rationale followed for the toroidal conformation, we assume
each loop to have a constant radius of curvature $R/2$ so that the bending and the
surface energy for the rod-like conformation have the following form

\begin{eqnarray}
\label{eq:eq22}
U_{rod} = \frac{32}{3} \kappa \eta\frac{R}{b} &\qquad
& \sigma S_{rod}= 2\pi \sigma R^2(\gamma+2) .
\end{eqnarray}

Use of Eq. (\ref{eq:eq21}) then leads to the following forms of the
bending energy and surface energy of the polymer in the rod-like condensate:
\begin{equation}
U_{rod} = \frac{32\kappa}{3}
\frac{\eta}
{\left[4\eta(\gamma+\frac{4}{3})\right]^{1/3}}
\left(\frac{L}{b}\right)^{1/3} ,
\label{eq:urod}
\end{equation}
\begin{equation}
\sigma S_{rod} = 2\pi (\sigma b^2) \frac{(\gamma+2)}
{\left[4\eta(\gamma+\frac{4}{3})\right]^{2/3}}
\left(\frac{L}{b}\right)^{2/3} .
\label{eq:srod}
\end{equation}
Again, like for the case of toroid condensate, we see that the surface energy
of the rod-like condensate is dominant over the bending energy in the large
$L$ limit.

\subsection{Interaction energy: polyvalent salts}
\label{subsec:interaction}

Up to this point we have not yet considered the actual interactions between neighboring polymer segments but our approach can be easily generalized to include them.
These interactions can be included on a general poor-solvent level \cite{Depletion}, on the detailed level of explicit electrostatic interactions \cite{Muthukumar2005} or on a phenomenological level based on experimentally determined effective potentials \cite{Todd}. We opt for the latter as the poor-solvent level seems to be too generic while the details of the exact DNA-DNA electrostatic interactions are still incompletely understood \cite{Cherstvy11}. An important reason for sticking to the phenomenological level is that the measured interactions of course contain all the interaction free energy contributions, including the water mediated hydration interaction \cite{Rau84} that do not feature explicitly in model expressions of the poor-solvent or indeed at the electrostatic level.

Let us consider toroidal geometry first and call the contribution of the
interactions between the molecules to the total free energy
\begin{equation}
\label{sec2:eq6b}
U_{int} = U_{int}(\alpha,\eta).
\end{equation}

The form of $U_{int}$ depends on the mode of condensation. In the case of
PSI-condensation it should include the depletion interaction contribution to
osmotic pressure and in the case of the polyvalent counterion condensation it
should include the "strong-coupling" attractive contribution to osmotic
pressure. In general we should have the pairwise interaction potential
between DNA segments to be {\it ``van der Waals-like''}, but without any
temperature dependence, since temperature is an irrelevant parameter in
condensation, being severely restricted to the interval between the melting of
DNA and freezing of the solvent \cite{footnote}.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig3.pdf}
\end{center}
\caption{Morse potential (Eq. \ref{morsebjko}) plotted with
parameters $d_0=2.8$ nm, $\lambda=0.48$ nm.
}
\label{fig:fig3}
\end{figure}

Let us first discuss DNA condensation in polyvalent salts. In this case the
interaction potential between two parallel neighboring segments of DNA at a
interaxial separation $d$ has been inferred from experiments \cite{Todd} and
has a form accurately described by a Morse potential
\begin{equation}
\widehat{\phi}(d) = \varepsilon \, e^{-2(d-d_0)/\lambda} -
2 \varepsilon \, e^{-(d-d_0)/\lambda} ,
\label{morsebjko}
\end{equation}
per unit length of the interacting straight segments. Here $\varepsilon$
defines the depth of the potential, $d_0$ is the equilibrium interaxial
distance between the molecules at which the potential has a minimum, and
$\lambda$ characterizes a characteristic length of the potential (see
Fig. \ref{fig:fig3}). Within this model $\varepsilon, d_0$ and $\lambda$
completely parametrize the interactions. For DNA condensation in
[Co(NH$_3$)$_6$]$^{3+}$, a good choice of parameters as inferred from
experiments \cite{Todd} is $d_0 = 2.8$ nm and $\lambda=0.48$ nm, and
$\varepsilon=0.21 k_BT$ per base pair.  Note that a base pair has a
length of $0.34$ nm so 1 $k_BT$/bp corresponds to about 2.94 $k_BT$/(nm).
Upon introducing $\phi(d)=\widehat{\phi}(d) b$, the total interaction energy
between all segments of the chain is then in general given by:
\begin{equation}
U_{int} = \sum_{i<j} \phi(d_{ij}) .
\end{equation}
As this is difficult to evaluate explicitly we introduce an approximation at
this point by considering only the segments that are nearest neighbors and
locally straight. This approximation works fine for short range interactions.
This yields
\begin{equation}
U_{int} \approx N_c \phi(d) ,
\label{eq:uint}
\end{equation}
where $N_c$ is the number of nearest neighbor pairs having distance $d$
between the  polymer segments.  For the assumed hexagonal local packing
symmetry the number of nearest neighbors per segment is 6 inside the condensate
and 4 on its surface.  As the interactions are partitioned between two
neighbors, each segment contributes only half of its interaction energy to the
total energy.  The total number of residues is $L/b$ whereas the number of
residues on the surface of the condensate equals to $S/(bd)$, where $S$
is the condensate's surface area. Thus the total $N_c$ can be estimated as:
\begin{equation}
N_c \approx  3\frac{L}{b} - \frac{S}{bd} .
\label{eq:Nc}
\end{equation}
Note that due to the surface term, $N_c$ depends on both
$d$ and geometrical parameter $\alpha$ or $\gamma$ depending on the
type of the condensate.

\subsection{Interaction energy: depletion forces}

For the PSI-condensation the effective interactions between polymer segments
include the depletion interaction contribution to osmotic pressure, which is
attractive, stemming from the flexible polymers in solution \cite{Depletion},
and acts on top of a short range repulsive interaction of either electrostatic
or hydration origin \cite{Curop}. The components of the interaction
energy should thus be a repulsive part and an attractive part that should look
like $-\Pi V_0$, where $\Pi$ is the osmotic pressure of the external polymer
solution and $V_0$ is the overlap of the excluded volume of DNA in the
condensate \cite{Depletion}:
\begin{equation}
U_{int} = U_{repulsion} - \Pi V_0 .
\end{equation}
Let's denote $\delta$ the size of the condensing agent molecule
(in our case the PEG). The overlap volume can be estimated as
\begin{equation}
V_0 = L\pi\left(\frac{b+\delta}{2}\right)^2 -
L\pi\left(\frac{b}{2}\right)^2 \frac{1}{\eta} - \frac{(b+\delta-d)S}{2} ,
\label{eq:V0}
\end{equation}
where the first term corresponds to the excluded volume of the polymer
in an open conformation, the second term corresponds to the
volume of the condensate (presumably to be fully excluded from the
osmoticants), the third term corresponds to the excluded
volume of the condensate's surface, and $S$ is the surface area of
the condensate (either toroidal or rod-like). Using Eq. (\ref{sec1:eq3}) one
can rewrite $V_0$ as follows
\begin{equation}
V_0 = L\pi\left(\frac{b+\delta}{2}\right)^2 -
L\pi\left(\frac{d}{2}\right)^2 \frac{1}{\eta_\text{hex}} -
\frac{(b+\delta-d)S}{2} .
\end{equation}
Note that $V_0$ should not be negative which implies that $V_0 \ge 0$
for $d \leq d_c$ with $d_c \approx b+\delta$, and $V_0=0$ otherwise. For a
given $L$ and $\alpha$, the maximum of $V_0$ is obtained at $d=b$.

The repulsive interaction part again contains the energy between all segments
of the chain. Just as before, we again consider only the segments that are
nearest neighbors and locally straight, an approximation that consistently
works for short range interactions. This again yields
\begin{equation}
U_{int} \approx N_c \phi_0(d) - \Pi V_0,
\label{depldw}
\end{equation}
with $\phi_0(d)$ the repulsive part of the Morse potential given
in Eq. (\ref{morsebjko}), i.e.
\begin{eqnarray}
\widehat \phi_0(d) & = & \varepsilon \, e^{-2(d-d_0)/\lambda} , \\
\phi_0(d) &=& b \, \widehat \phi_0(d) .
\label{eq:phi0}
\end{eqnarray}
The osmotic pressure $\Pi$ is given in units of $k_B T/$(unit
length)$^3$. This form of the interaction potential is
routinely seen when compressing DNA with osmoticants such as PEG \cite{RP1}
and is shown on Fig. \ref{fig:fig4}.
The parameters in the repulsive part pertain either to the electrostatic or
hydration interaction, while the osmotic pressure of PEG is known from its
equation of state \cite{Joel}.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig4.pdf}
\end{center}
\caption{Depletion potential (Eq. \ref{depldw}) calculated for toroidal
condensate with parameters for the repulsive potential $d_0=2.8$ nm,
$\lambda=0.48$ nm; the size of osmoticant $\delta=4$ nm; and the osmotic
pressure $\Pi=1\varepsilon/$(nm)$^3$. The dependence on distance $d$ between
nearest neighbor
segments is shown for $U_{int}/N_c$ (solid line), $\phi_0(d)$ (dashed line) and
$-\Pi V_0/N_c$ (dotted line) as indicated.  Note that the position and the
depth of the minimum depends on the value of $\Pi$.}
\label{fig:fig4}
\end{figure}

\section{Results}

We now present the results of minimization of the different energy {\sl
Ans\"atze} for a polymer of length $L$. For the toroid-like aggregate with mean
radius $R$ and the thickness $\Delta=\alpha R$ the minimization of
$E_{toroid}(\alpha)$ should be with respect to $\alpha$. For the rod-like
spherocylindrical condensate with circular cross-section of radius $R$ and
length $\gamma R$ the minimization of $E_{rod}(\gamma)$ should be with respect
to $\gamma$. In both cases we first consider the constrained system
with a fixed volume fraction.
We later relax the constraint and consider a system with a soft
interaction potential
(either the Morse potential or the depletion potential)
that depends on the density of the system. In this case an additional
minimization with respect to the nearest neighbor separation $d$, or
equivalently the density of the system, is in order in both
$E_{toroid}(\alpha,d)$ and $E_{rod}(\gamma,d)$.

\subsection{Condensates with surface tension}

We first consider an energy {\sl Ansatz} which is composed of the bending energy term
and the surface term only. We assume that the packing fraction $\eta$ is
constant for both the toroidal and rod-like condensate.

For the toroidal condensate, the total energy reads:
\begin{equation}
E_{toroid} (\alpha) = U_{toroid} (\alpha) + \sigma S_{toroid} (\alpha) ,
\label{eq:etot1}
\end{equation}
where $\sigma$ is the surface tension; $U_{toroid}$ and $S_{toroid}$ are given
in Eq. (\ref{sec2:eq6}) and Eq. (\ref{eq:storoid}), respectively. This energy
is dependent both upon the geometry of the torus through the parameter
$\alpha$, the we can seek the optimal configuration by minimizing this energy
with respect to $\alpha$ at fixed $L$. This minimization leads to the condition
\begin{equation}
\left .
\frac{\partial E_{toroid}}{\partial \alpha} \right |_{\alpha=\alpha^*} = 0
\end{equation}
which yields
\begin{eqnarray}
\label{eq:alpha_star}
\alpha^{*} &=& \frac{1}{8^{3/5}}
\frac{\pi^{2/5}}{\eta^{4/5}}
\left(\frac{\sigma b^2}{\kappa}\right)^{3/5}
\left(\frac{L}{b}\right)^{1/5}.
\end{eqnarray}
The minimum energy $E_{toroid}^{*}\equiv E_{toroid}(\alpha^{*})$
corresponds to the case where surface and bending energy become comparable and
can be obtained from Eq. (\ref{eq:etot1}) as
\begin{eqnarray}
\label{sec2:eq9}
E_{toroid}^{*}&=& \left(\sigma b^2\right) \frac{5}{2^{7/5}}\frac{\pi^{6/5}}
{\eta^{2/5}} \left(\frac{\kappa}{\sigma b^2}\right)^{1/5}
\left(\frac{L}{b}\right)^{3/5} .
\end{eqnarray}
Thus the energy of the toroid is minimum when $\alpha=\alpha^*$ if $\alpha^* <
1$ and $\alpha=1$ otherwise. As discussed before, the latter corresponds to a
``globular state''.
From Eq. (\ref{sec2:eq9}) it is easily seen that both $\alpha^*$ and
$E_{toroid}^*$ are minimum when $\eta$ is maximum. Thus, if $\eta$ is
allowed to vary a further minimization with respect to $\eta$
yields a minimum energy that corresponds to $\eta=\eta_\text{hex}$.

Note that, for any fixed $\kappa/(\sigma b^2) \ge 0$, the ``globule'' will be
the lower energy state as the bending energy is always sub-leading with respect
to the surface energy in the limit  $L/b \gg 1$.  Conversely, for a finite
length $L/b>0$ there will be a critical $\kappa$ beyond which the curvature
term will be dominant. From Eq. (\ref{eq:alpha_star}) this is clearly the case
when $\kappa/(\sigma b^2)$ is large enough so that  $\alpha^* < 1$. This
provides the condition
\begin{equation}
\frac{\kappa}{\sigma b^2} > \frac{1}{8} \frac{\pi^{2/3}}{\eta^{4/3}}
\left(\frac{L}{b}\right)^{1/3} .
\label{eq:glob}
\end{equation}
This implies a $L^{1/3}$ law for the phase separation between the toroid and
the globule. However, as we will show later in this Subsection, for $\kappa>0$
the globule is always unfavorable against the rod-like condensate, so that in
reality the transition line from a toroid to a globule does not exist in the
ground state phase diagram, if one also takes into account the rod-like
configuration of the condensate.

On the other hand, one also requires that the energy of the toroid be smaller
than the energy of the swollen phase which can be approximated with a straight
line conformation:
\begin{equation}
E_{toroid}^{*} < E_{swollen} = \sigma b^2  \pi \frac{L}{b}.
\end{equation}
In the above equation the surface area of the swollen conformation is assumed
to scale as that of a cylinder of length $L$ and diameter $b$. Note that this
conformation has no bending penalty. From Eq. (\ref{sec2:eq9})
one obtains
\begin{equation}
\label{eq:quadratic_line}
\frac{\kappa}{\sigma b^2} < \frac{2^7}{5^5} \frac{\eta^{2}}{\pi}
\left(\frac{L}{b}\right)^{2} .
\end{equation}
The right-hand term of Eq. (\ref{eq:quadratic_line}), yields the dashed line
shown in Fig. \ref{fig:fig5}, above which the bending energy is so large that
the swollen phase is clearly the only optimal conformation.

\begin{figure}[htbp]
\begin{center}
 \includegraphics[width=3.4in]{Fig5.pdf}
\end{center}
\caption{Expected phase diagram on the basis of the theoretical analysis for
the toroidal, rod-like and swollen phase. The phase diagram was computed
numerically for the maximum packing fraction $\eta=\eta_\text{hex}$ of the
toroidal and rod-like condensates. The toroidal phase is favorable with
respect to the rod-like counterpart above a certain stiffness, and on the right
of the swollen phase.  The transition line from toroid to swollen (dashed line)
has a $L^2$ dependence as given by Eq. (\ref{eq:quadratic_line}).  The
transition points from toroid to rod-like have been determined numerically from
the condition $E_{toroid}^{*}=E_{rod}^{*}$ (open circles)  and are very well
fitted by a $L^{1/3}$ dependence (solid line).
}
\label{fig:fig5}
\end{figure}

The energy of the rod-like condensate is given by
\begin{equation}
E_{rod} (\gamma) = U_{rod} (\gamma) + \sigma S_{rod} (\gamma) ,
\label{eq:erod1}
\end{equation}
where $U_{rod}$ and $S_{rod}$ are given in Eq. (\ref{eq:urod}) and Eq.
(\ref{eq:srod}), respectively. $E_{rod}$ depends on the geometry of the
spherocylinder  through the parameter $\gamma$, thus we can obtain the optimal
configuration by minimizing this energy with respect to $\gamma$ at fixed $L$.
This yields
\begin{eqnarray}
\label{eq:eq26}
\frac{(\gamma^* + \frac{4}{3})^{1/3}}{\gamma^*} &=& \frac{3\pi}{4^{7/3}
\eta^{4/3}}
\left(\frac{\sigma b^2}{\kappa} \right)
\left(\frac{L}{b}\right)^{1/3} .
\end{eqnarray}
The $\gamma^*=0$ solution (the globule) exists only in the limit of $\kappa=0$,
i.e.  non-stiff chain. Thus for semiflexible chains ($\kappa>0$), the rod-like
structure is always energetically favored against the globule and no phase
transition exists  between the rod-like and the globule phases.

The ``ground-state'' energy for the rod-like structure can then be obtained as
$E_{rod}^{*}=E_{rod}(\gamma^{*})$, and compared with the toroid counterpart
$E_{toroid}^{*}$. This provides the full phase diagram in the stiffness-length
plane depicted in Fig. \ref{fig:fig5}, where a transition from a rod-like to a
toroidal conformation is obtained upon increasing $\kappa/(\sigma b^2)$ at a
fixed length.  Remarkably, the transition line from the toroid to a rod-like
condensate follows a $L^{1/3}$ law as revealed by numerical data (Fig.
\ref{fig:fig5}).  The exact location of the intermediate swollen phase,
appearing in Fig. \ref{fig:fig5} for very short lengths, is outside of the
range of applicability of our analysis and it would require further more
specific analysis.

\subsection{Monte Carlo simulations}

We can now compare the scenario obtained by analytical approximations with that
obtained from detailed simulations. To this aim, we have implemented a
standard NVT Monte Carlo simulations on a bead-stick model, where the
DNA chain is modeled as a collection of $N$ consecutive monomers represented
by impenetrable hard spheres of radii $R_{HS}=b/2$ that are tangent to each
other, while the non-consecutive monomers interact via a square-well potential
of range $R_{int}=1.3 b$. We have studied systems of lengths $L$ up to 96
monomers
and stiffness $\kappa$ up to 50$\epsilon$, where $\epsilon$ is the depth
of the square-well potential. An extensive search for the ground states has
been performed in order to construct a phase diagram in the $\kappa$-$L$ space.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig6.pdf}
\end{center}
\caption{
Phase diagram obtained from Monte Carlo simulations displaying toroid and
rod-like ground state energies.  The range of the square-well interaction
was selected to be $R_{int}=1.3 b$, and $R_{HS}=b/2$ is the radius of each
monomer. Underlying broken lines represent a fit of the $(L/b)^{1/3}$
(dotted line) and $(L/b)^2$ (dashed line) dependences found in Fig.
\ref{fig:fig5}.
}
\label{fig:fig6}
\end{figure}

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig7.pdf}
\end{center}
\caption{Snapshots of the toroidal and rod-like configurations obtained in simulations
of the bead-stick model.  The conformations shown are the lowest energy
conformations for
$N=48$ and $\kappa=10\epsilon$ (a),
$N=48$ and $\kappa=6\epsilon$ (b),
$N=96$ and $\kappa=11\epsilon$ (c),
$N=96$ and $\kappa=9\epsilon$ (d).
}
\label{fig:fig7}
\end{figure}

The simulations are carried out with standard pivot and crankshaft move sets
and the Metropolis algorithm for move acceptance. A parallel tempering scheme
with 16 replicas is implemented to efficiently equilibrate the system and to
obtain the ground state and low energy conformations at low temperatures.
Consistent results are typically obtained after $1 \div 10\times 10^9$ MC
steps per replica depending on the chain length.

The resulting phase diagram shown in Fig. \ref{fig:fig6} is in remarkable
agreement with Fig. \ref{fig:fig5}, thus confirming the soundness of our
analytical theory. We also present snapshots illustration of toroidal and rod-like
conformations  in Fig. \ref{fig:fig7}.

Very recently, a molecular dynamic study by Lappala and Terentjev appeared
\cite{Lappala13} where they also observed a transition from rod-like to
toroidal condensate above a well defined  persistence length, in full agreement
with our results.

\subsection{Condensates with soft interactions: polyvalent salts}

We now proceed to include the soft interactions between the polymer segments
in the condensate instead of the surface tension, as anticipated earlier. As we
shall see, there will be some general consequences that are independent of the
specific functional form of the interaction potential pointing towards a
universality of the condensation phenomenon in semiflexible polymers.

For the toroidal case the energy {\sl {\sl Ansatz}} is
\begin{eqnarray}
E_{toroid}\left(\alpha, \eta \right) &=&  U_{toroid} (\alpha,\eta)
+ U_{int}(\alpha, \eta) \nonumber \\
&=&  U_{toroid} (\alpha,\eta) - \frac{\phi(d)}{bd} S_{toroid} (\alpha,\eta) +
\nonumber \\
& & + 3\phi(d)\frac{L}{b} \ ,
\end{eqnarray}
where where $U_{int}(\alpha,\eta)$ given in Eq. (\ref{eq:uint}) is the
interaction part depending on the density of the molecules, and
$\phi(d)$ is the Morse potential given in Eq. (\ref{morsebjko}).
The explicit forms of $U_{toroid} (\alpha,\eta)$ and $S_{toroid} (\alpha,\eta)$
are given in Eq. (\ref{sec2:eq6}) and Eq. (\ref{eq:storoid}), respectively.
Note that $\eta$ depends on $d$ by Eq. (\ref{sec1:eq3}) so that
these two parameters are equivalent.
Analogously for the
rod-like condensate case the energy {\sl {\sl Ansatz}} is
\begin{eqnarray}
E_{rod}\left(\gamma, \eta \right) &=&  U_{rod} (\gamma,\eta)
+ U_{int}(\gamma, \eta) \nonumber \\
&=&  U_{rod} (\gamma,\eta) - \frac{\phi(d)}{bd} S_{rod} (\gamma,\eta) +
\nonumber \\
& & + 3\phi(d)\frac{L}{b} \ ,
\end{eqnarray}

For a fixed value of density, or equivalently $d$, one can find a minimum of
$E_{toroid}\left(\alpha, \eta \right)$ with respect to $\alpha$. This gives
\begin{eqnarray}
\label{eq:alpha}
\alpha^{*} &=& \frac{1}{8^{3/5}}
\frac{\pi^{2/5}}{\eta^{4/5}}
\left(\frac{\sigma' b^2}{\kappa}\right)^{3/5}
\left(\frac{L}{b}\right)^{1/5} ,
\end{eqnarray}
where $\sigma' = - \frac{\phi(d)}{bd}$ and $\eta=\eta_{\text{hex}}
\left(\frac{b}{d}\right)^2$. Note that we look only for solution of $\alpha$ in
the range of [0,1]. So $\alpha^* < 0$ corresponds to $\alpha^*=0$ (swollen
conformation) and $\alpha^*>1$ corresponds to $\alpha^*=1$ (globule
conformation).

In the case of the rod-like condensate we get analogously the equation
for $\gamma^*$:
\begin{equation}
\label{eq:gamma}
\frac{(\gamma^* + \frac{4}{3})^{1/3}}{\gamma^*} = \frac{3\pi}{4^{7/3}\eta^{4/3}}
\left(\frac{\sigma' \, b^2}{\kappa} \right)
\left(\frac{L}{b}\right)^{1/3} .
\end{equation}
If $\sigma' < 0$, there is no solution of $\gamma^* > 0$, the minimum of
$E_{rod}$ is obtained at $\gamma^*=\infty$ (swollen conformation). If $\sigma'
> 0$, a solution $\gamma^* > 0$ always exists if the right hand side is finite.

In order to calculate the phase diagram, we need to compare the minimum energy
of the toroidal condensate with that of the rod-like condensate. The analysis
is pretty similar to that in the previous section with $\sigma'$ playing the
role of surface tension, except that we have now the interaction energy
$\phi(d)$ between polymer segments (and so is $\sigma'$) depending on the
interchain distance $d$ between nearest neighbors. Thus, the minimization of
the energy should be done also with respect to $d$, or equivalently to $\eta$.
It is convenient to do the minimization numerically for both the toroidal and
the rod-like condensates.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig8.pdf}
\end{center}
\caption{Separation between the toroid phase and the rod-like phase
as predicted by our theoretical model
with the Morse interaction potential. The transition line was
calculated numerically and is fitted very well by a $L^{1/3}$ law.
The depth of the interaction potential
is chosen to be $\varepsilon=0.21 k_BT$/bp.  The horizontal line
corresponds to DNA stiffness, $\beta \kappa = l_p/b = 25$,
the DNA diameter $b=2$ nm and persistence length $l_p=50$ nm.
The cut-off length for the toroid is
$L_c=18.6\times10^3b$ or equivalent to 109.4 kbp.
}
\label{fig:fig8}
\end{figure}

Fig. \ref{fig:fig8} shows the phase diagram in the stiffness-length plane
obtained for realistic parameters of the Morse potential. The latter (shown in
Fig. \ref{fig:fig3}) is calculated with $b=2$ nm (the diameter of DNA), $d_0 =
2.8$ nm (the equilibrium interaxial distance between neighboring base pairs),
$\lambda=0.48$ nm (the width of the potential), $\varepsilon = 0.21 k_BT$/bp
(the depth of the potential). The phase separation line behaves like $L^{1/3}$,
as in the model with only the bending energy term and the surface term. Using a
realistic parameter for DNA stiffness, $\kappa=25 k_BT$, it is found that the
critical length $L_c$ for the toroid is equivalent to 109.4 kbp. For
$L>L_c$ the ground state becomes the rod-like structure.

Fig. \ref{fig:fig9} (Top) shows the numerical solutions for the toroid
geometrical parameter $\alpha^{*}$ as function of the chain length $L$ for
realistic parameters of DNA. We find that $\alpha^*$ grows with the chain
length like $L^{1/5}$ up to a maximum value $\alpha^*_c \approx 0.807$ at the
phase separation ($L=L_c$). We have also found that the value of $\alpha^*_c$
does not depend on the chain stiffness and interaction energy parameter.
Further in Fig. \ref{fig:fig9} (Bottom), the dependence of the
toroid radius $R$ and thickness $\Delta=\alpha R$ on the total contour length
$L$ of the DNA is also depicted. The toroid radius is found to grow with the
chain length like $L^{1/5}$ whereas its thickness grows like $L^{2/5}$.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig9.pdf}
\end{center}
\caption{(Top) Numerical solution of Eqs. (\ref{eq:alpha}) as a function of the
chain length. (Bottom) The corresponding growth of toroid radius, $R$, and
toroid thickness, $\Delta$ with chain length, $L$, that can be fitted by a
$L^{1/5}$ law for the radius and a $L^{2/5}$ law for the thickness,
respectively. The dependences are shown for $L<L_c$.
The data are obtained for the model with Morse interaction
potential with realistic parameters for DNA with $\epsilon=0.21 k_B T$/bp.
}
\label{fig:fig9}
\end{figure}

An interesting finding of our theoretical analysis concerns a prediction of the
toroid thickness's dependence on the toroid radius, as illustrated in Fig.
\ref{fig:fig10}, and is in very good agreement with the experimental findings of
Conwell et al. \cite{Conwell03}. Our results clearly shows that the ratio of
the toroid diameter to toroid thickness strongly depends on the solvent
condition as given by the energy parameter $\varepsilon$. The poorer the
solvent, the smaller is the toroid diameter.  Our model could be used to
infer the interaction energy between base pairs from experimental data of toroid
sizes for various solvent conditions.
Furthermore, for a given value of $\epsilon$, our model indicates that (toroid diameter) $ \propto $ (toroid thickness)$^{1/2}$. This
relation could be verified experimentally by direct measurements of toroid dimensions.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig10.pdf}
\end{center}
\caption{Toroid thickness ($=2 \alpha R$) vs. toroid diameter ($=2 R$) as predicted by our theoretical
model for several values of interaction energy parameter $\varepsilon$ as
indicated. The toroid thickness and diameter are calculated for length $L<L_c$
at which the toroid is the ground state. The DNA parameters used here were
$b=2$ nm, $d_0=2.8$ nm, $\lambda=0.48$ nm, and $\kappa=25 k_B T$.
}
\label{fig:fig10}
\end{figure}

\subsection{Condensates with soft interactions: depletion potential}

We consider now the third energy {\sl Ansatz} in which the energy of the condensate
is composed of the bending energy and the interaction energy due to osmotic
depletion. For the toroidal condensate, the energy takes the following form:
\begin{equation}
E_{toroid} (\alpha,d) = U_{toroid} (\alpha,d) + N_c \phi_0(d)
- \Pi V_0 (\alpha,d) ,
\end{equation}
where $N_c$ is given in Eq. (\ref{eq:Nc}) and $V_0$ is given in Eq.
(\ref{eq:V0}). It is straightforward to show that for a given $d$, the energy
is minimized at the value of $\alpha^*$ given by
\begin{eqnarray}
\label{eq:alphadep}
\alpha^{*} &=& \frac{1}{8^{3/5}}
\frac{\pi^{2/5}}{\eta^{4/5}}
\left(\frac{\sigma' b^2}{\kappa}\right)^{3/5}
\left(\frac{L}{b}\right)^{1/5} ,
\end{eqnarray}
with $\sigma' = \Pi\frac{b+\delta-d}{2}- \frac{\phi_0(d)}{bd}$.
Similarly for the rod-like condensate, the equation for $\gamma^*$ is the same
as Eq. (\ref{eq:gamma}) with the new $\sigma'$ as in the above equation.
Note that in order for the toroid to be stable, $\sigma'$ should be positive,
this leads to the following condition for the osmotic pressure:
\begin{equation}
\Pi \geq \min_{d<b+\delta} \ \frac{2\phi_0(d)}{bd(b+\delta-d)} = \Pi_{min},
\end{equation}
where the minimum is taken over all $d$ satisfying $d<d+\delta$. This minimum
value of the osmotic pressure strongly depends on the diameter of the
osmoticant. For example, for the repulsive interaction given in Eq.
(\ref{eq:phi0}) with realistic parameters for DNA, $\Pi_{min} \approx
2.2$ $k_BT$/(nm)$^3$ and $0.025$ $k_BT$/(nm)$^3$ for $\delta=1$ nm
and 2 nm, respectively. So with a small osmoticant it is much harder to
condense DNA than with larger ones. Note that an effective diameter of $2$ nm
would correspond to PEG-6000 as an osmoticant.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig11.pdf}
\end{center}
\caption{Phase separation between the toroid and the rod-like structure in the
$\kappa$-$L$ diagram for two values of osmotic pressure $\Pi$ as indicated.
The numerical data (squares and circles) can be fitted very well with
$L^{1/3}$ (solid and dashed lines) for both cases.
}
\label{fig:fig11}
\end{figure}

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig12.pdf}
\end{center}
\caption{
Dependence of toroid diameter on toroid thickness in the model with
depletion potential. The data are shown for three values of osmotic
pressure $\Pi$ as indicated.
}
\label{fig:fig12}
\end{figure}

Figs. \ref{fig:fig11} and \ref{fig:fig12} show the phase diagram and the
dependence of toroid diameter on toroid thickness for the case with depletion
potential. Note that phase separation line well follows the $L^{1/3}$ law,
and the stronger osmotic pressure, the smaller sizes of toroids are formed.
The results are qualitatively similar to those obtained with the
Morse potential and the hard-core interaction case.  Therefore the detailed
form of the interaction potential, while being important for the equation of
state of DNA \cite{Strey99}, has only a small effect on the location of the
transition lines and on the length dependence of the various phases themselves.

\subsection{Nonlinear elasticity: stiff chain with an elastic threshold}

Up to now we have only considered the variations in the interaction potential
on the phase diagram of the condensate. Inspired by the tube model of a polymer
\cite{Maritan00,Banavar03,Poletto08}, we finally also consider a variation in
the form of the bending energy of the polymer. Specifically we intend to
introduce modifications in the $\theta$ dependence of the curvature energy.

Assume first that the curvature energy vanishes for $\theta \leq \theta_0$  and
becomes $\infty$ otherwise. The ensuing radius of curvature is in this case also limited
by a corresponding lower bound $R_0$
\begin{equation}
\label{sec4:eq1}
1 - \cos \theta = \frac{b^2}{2 R^2} < 1 - \cos \theta_0 \ ,
\end{equation}
or
\begin{equation}
\label{sec4:eq2}
R > \frac{b}{\sqrt{2\left(1-\cos\theta_0\right)}} \equiv R_0 \ .
\end{equation}

Under  these assumptions, the polymer will try to make very large turns (i.e.
large radius of curvature) in order to have $U=0$. Hence a rod-like structure,
where short turns are unavoidable, will then be consequently highly
unfavorable, as further elaborated below.

When the condition (\ref{sec4:eq2}) is met, the total energy coincides with
surface energy only, so that
\begin{eqnarray}
\label{sec4:eq3}
E_{toroid} (\alpha) & = & \sigma S_{toroid} =  \sigma b^2 4 \pi^2 \alpha
\left(\frac{R}{b}\right)^2 \nonumber \\
 &=& \left(\sigma b^2\right) \frac{\pi^{4/3}}{\alpha^{1/3} \eta^{2/3}} \left(\frac{L}{b}\right)^{2/3} ,
\end{eqnarray}
in the same form as given in Eq. (\ref{eq:storoid}). From the above
equation one can see that for a given length $L$ the minimum energy is obtained
when both $\eta$ and $\alpha$ are at their maximum values, i.e.
$\eta=\eta_\text{hex}$ and $\alpha=\alpha^*$. On the other hand,
from Eq. (\ref{eq:Rb}) it is clear that for a given $L$, $\alpha$ is
maximum when $R$ is minimum, thus one obtains the following equation
for $\alpha^*$:
\begin{equation}
\frac{L}{b} = 8\pi\eta_\text{hex} (\alpha^*)^2 \left(\frac{R_0}{b}\right)^2 .
\end{equation}
The above equation has a solution $\alpha^* < 1$ only if
\begin{equation}
L < L_0 \equiv 8\pi\eta_\text{hex} b \left(\frac{R_0}{b}\right)^2 .
\label{eq:LL0}
\end{equation}
In other words, the toroid can be a minimum energy configuration only when
$L<L_0$. For $L\geq L_0$ the minimum energy would be a globule ($\alpha^*=1$).
Because there is no bending energy, the globule would be always favored
compared to the rod-like conformation, having the lowest surface energy. It
then follows that within this model, only two phases are possible: the toroid
phase for length $L < L_0$ and the globule phase for $L > L_0$ (see Fig.
\ref{fig:fig11}). Here $L_0$ is the smallest length necessary to form a globule
and can be determined from Eqs. (\ref{eq:LL0}) and (\ref{sec4:eq2}) as
\begin{eqnarray}
\label{sec4:eq5}
\frac{L_0}{b} &=& \frac{2^{3/2}\pi \eta_{\text{hex}}}{\left(1-\cos\theta_0\right)^{3/2}} .
\end{eqnarray}

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=3.4in]{Fig13.pdf}
\end{center}
\caption{
Ground state phase diagram for a stiff chain with a threshold on
angle $\theta$. Solid line is where $L=L_0$.}
\label{fig:fig13}
\end{figure}

For $L<L_0$ it is easy to show that
\begin{equation}
\label{sec4:alpha}
\alpha^* = \left(\frac{L}{L_0}\right)^2 ,
\end{equation}
and
\begin{equation}
\label{sec4:etormin}
E_{toroid}^{*} = \left(\sigma b^2\right)
\frac{\pi^{4/3}}{\eta_{\text{hex}}^{2/3}}
\left(\frac{L_0}{b}\right)^{1/6}
\left(\frac{L}{b}\right)^{1/2} .
\end{equation}
We have also checked by extensive simulations that the ground state of a
self-attracting polymer with a threshold on angle $\theta$ is  a toroid (data
not shown) for the chain length $L<L_0$ in accordance with the phase diagram
shown in Fig. \ref{fig:fig13}.

\section{Conclusions}

We have studied the phase diagram of semi-flexible polymers with
self-attraction as a function of the stiffness and the contour length of the
chain. This is a prototypical model for DNA condensation, a problem with a long
history that is still not completely understood.

We have combined analytical arguments with extensive Monte Carlo simulations, to study the competition between toroidal and rod-like configurations as candidates for the ground state of the condensate at increasing stiffness of the polymer molecules. As the stiffness increases, we find an increasing tendency for the polymers to achieve a nematic alignment in order to minimize the bending energy. This typically favours first a transition from a globular to a rod-like conformation, and then a further transition to a toroidal conformation that is then the most stable one at sufficiently large stiffness values. This scenario appears to be rather robust irrespective of the details of the interaction potential between the segments of the molecules, provided that the polymer chain is sufficiently long.

In the stiffness-length plane, we furthermore found a robust $L^{1/3}$ dependence of the transition line between the rod-like and the toroidal phases, that  can be simply explained within our analytical approach. An additional $L^{1/5}$ dependence was also observed for the toroid radius. While the existence of some of these scaling laws has been known for some time, see the work of Grosberg and Zhestkov Ref. \onlinecite{history}, a comprehensive analysis combining an analytical approach with numerical simulations has been, to the best of  our knowledge, still missing. Our work fills this gap.

Finally, our conclusions are in good agreement also with very recent molecular dynamics simulations \cite{Lappala13} that studied the dynamics of a polymer chain collapse in poor solvents as a function of the chain flexibility. We assessed the importance of the exact form of the interaction potential, as extracted from experiments, while constructing models for polyvalent salt condensed DNA as well as polymer and salt induced DNA condensation. We also investigate the effects of non-linear elasticity within the specific model of a tube model of a polymer that has important consequences on the phase diagram of the semi-flexible chain.

\section{acknowledgments}
AG acknowledges funding from  PRIN-COFIN2010-2011 (contract 2010LKE4CC).
TXH and NTTN thank for support from National Foundation for Science and Technology Development (NAFOSTED Grant 103.01-2010.11). RP acknowledges support from the Agency for Research and Development of Slovenia (ARRS grant P1- 0055(C)).

redpajama_set_name: RedPajamaArXiv


Boasting awesome CGI effects and beguiling images, director Ang Lee's adaptation of Yann Martel's bestseller about shipwreck and survival matches the book for wonder. You really will believe that resilient young hero Pi (Suraj Sharma) is stranded on a lifeboat along with a tiger. The film's marvellous sequences include a mirror-like sea reflecting golden clouds, a swarm of flying fish, an island bristling with meerkats and a whale leaping out of the water. This not to be missed epic deservedly won Oscars for direction, cinematography, effects and score.


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Book Sir Geoff Hurst
ONLY PLAYER EVER TO RECORD A HAT TRICK IN A WORLD CUP FINAL AND MEMBER OF THE WORLD CUP WINNING ENGLAND TEAM IN 1966
Sir Geoff Hurst MBE is a retired football player who will be most remembered for being a part of England's 1966 World Cup winning squad. Arguably one of the greatest strikers from his generation, Hurt is a legend of the game and is a hero to thousands across the world. Once retiring, Hurst became a manager and managed Chelsea for two years. As well as football, Hurst had a brief spell playing county cricket for Essex but soon gave up to concentrate on football.
Spending a lot of his time as a football speaker, Hurst often reflects on his magnificent career and discusses vital sport and business topics like performing under pressure. He played the majority of his career with West Ham United where he played 411 games scoring an astonishing 180 goals. He also played for Stoke City and West Bromwich Albion before spending time abroad for different clubs. Overall, Hurst played 561 club games scoring an amazing 228 goals highlighting his incredible finishing ability.
During his time with West Ham, Hurst won the FA Cup and the European Cup Winners' Cup . As an individual, he was named Hammer of the Year on three occasions and featured in the World Soccer World XI in three consecutive years between 1967 and 1969. Winning such prestigious awards showcased his incredible talent as a footballer, he had an eye for goals and scored many wherever he played. As a speaker he often discusses topics like achieving goals and maximising success as he showcased how to do both of these throughout his career.
Hurst played a significant part during the 1966 World Cup , he scored the only goal in a quarter-final win against Argentina before starting the final. England drew 2-2 in normal time after Hurst put them 1-0 up, this meant the final went to extra time. During extra time, Hurst scored two goals to give England a 4-2 victory and Hurst a hat trick in a World Cup final. This showcased just how special Hurst was as a player and also his ability to perform under pressure, a topic he passionately speaks about as a speaker.
His wonderful knowledge of football and expertise in a number of business-related topics make him a unique, yet incredible football speaker. Hurst can inspire audiences with ease and speaks with lots of wisdom which makes him a truly compelling speaker.
How to hire Sir Geoff Hurst
Contact the Champions Speakers agency to provisionally enquire about Sir Geoff Hurst for your event today. Simply call a booking agent on 0207 1010 553 or email us at [email protected] for more information.
When at corporate events, Sir Geoff is known to cover the following topics:
Drive & Determination
Performing Under Pressure
Sporting Success
Team Motivation
Maximising Success
Similar speakers to Sir Geoff Hurst
1966 World Cup Winner & Manchester United Legend
One Of England's Greatest Ever Footballers Turned England Manager & Pundit
One Of Nine Players To Score 150 Goals In The Premier League Who Was Also Capped 89 Times For England (Scoring 40 Goals)
Iconic Liverpool Footballer, Media Personality & Brilliant Speaker Who Was As England's 'Greatest Ever Left-Footed Player' By The Times' Readers
Exclusive Interview: Sir Mo Farah CBE – Olympic, World & European Champion Named the UK's Greatest Ever Athlete
Interviews, Olympics, Sports

redpajama_set_name: RedPajamaCommonCrawl


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Neil Riordan PhD
Professional Site
Mesenchymal Stem Cells
Invited Reviewer
Home Uncategorized Umbilical Cord Mesenchymal Stem Cells as Preeclampsia Treatment
Umbilical Cord Mesenchymal Stem Cells as Preeclampsia Treatment
Posted on March 29, 2016 Written by nhriordan 3 Comments
Treatment with human umbilical cord mesenchymal stem cells is shown to be effective in controlling hypertension and reducing the infiltration of inflammatory cells in the placenta, in this preeclampsia rat model.
Reprod Sci. 2016 Feb 17. pii: 1933719116630417.
Effect of Human Umbilical Cord Mesenchymal Stem Cell Transplantation in a Rat Model of Preeclampsia.
Wang LL, Yu Y, Guan HB, Qiao C.
OBJECTIVE: To test the effects of human umbilical cord mesenchymal stem cell (HU-MSC) transplantation on reversing preeclampsia (PE) symptoms in a lipopolysaccharide (LPS)-induced rat PE model.
METHODS: Human umbilical cord MSCs were detected, isolated, and cultured. Human umbilical cord MSC transplantation was conducted. Expressions of inflammatory cytokines in serum and placental tissue were measured by enzyme-linked immunosorbent assay. Changes in inflammatory cytokines, peroxisome proliferator-activated receptor γ (PPARγ), laminin receptor 1 (LR1), matrix metalloproteinase (MMP) 2, and MMP-9 messenger RNA (mRNA) levels in placental tissue were recorded by quantitative real-time polymerase chain reaction. Immunohistochemistry and Western blotting were performed for PPARγ detection.
RESULTS: The LPS group exhibited increased blood pressure and proteinuria and decreased fetal weight compared to the normal pregnancy (NP) group (all P < .05). The LPS + MSC group presented lowered blood pressure and higher fetal weight than the LPS group (P < .05). The levels of interferon γ, tumor necrosis factor α (TNF-α), interleukin (IL) 1β, IL-6, IL-8, IL-12, and intercellular adhesion molecule 1 (ICAM-1) increased and the levels of IL-4 and IL-10 levels decreased in the LPS group compared to the NP group (all P < .05). Tumor necrosis factor α, IL-6, IL-12, and ICAM-1 levels decreased and IL-10 level increased in the LPS + MSC group compared to the LPS group (all P < .05). The LPS-MSC group showed lower mRNA expressions of TNF-α, IL-6, MMP-2, MMP-9, and ICAM-1 and higher mRNA expressions of IL-10, PPARγ, and LR1 than the LPS group (all P < .05).
CONCLUSION: In summary, HU-MSC transplantation may be extremely beneficial for PE therapy.
© The Author(s) 2016.
Filed Under: Uncategorized Tagged With: mesenchymal stem cells, preeclampsia, stem cells, umbilical cord
robert perryman says
I don't see any info on neuropathy treatment . Is that an option?
nhriordan says
Stem Cell Therapy for Neuropathic Pain: New Findings Show Promise
Animal studies demonstrate effectiveness
Stem cell research at Cleveland Clinic could pave the way for an entirely new approach to chronic pain treatment that reduces medicine's current reliance on opioid therapy for intractable pain. The modality also shows promise as a tool to reverse opioid tolerance (OT) and opioid-induced hyperalgesia (OIH), particularly problematic side effects of opioid therapy. Jianguo Cheng, MD, PhD, and his colleagues at Cleveland Clinic have developed patented methods of attenuating opioid tolerance.
Animal studies by Dr. Cheng and his colleagues have demonstrated the effectiveness of mesenchymal stem cell (MSC) transplantation in reducing hyperalgesia due to nerve injury. The group's work has shown MSC transplantation's effectiveness in reducing pain induced by sciatic nerve injury in rats and mice. MSC transplantation significantly reduced pain sensitivity evaluated by foot withdrawal thresholds in animals in response to thermal or mechanical stimulation. These cells produced immune modulatory and anti-inflammatory effects, promoted sensory nerve repair, and showed strong analgesic properties that could provide a safer and more effective alternative to current treatment modalities, in the management of neuropathic pain, says Dr. Cheng, Professor of Anesthesiology and Director of the Cleveland Clinic Multidisciplinary Pain Medicine Fellowship Program.
Pain medicine researchers are searching for an alternative to opioid therapy because neuropathic pain often does not respond to morphine and other opioids. Opioid analgesics can also lead to a variety of complications, ranging from itching and constipation to dependence, addiction, respiratory depression and death.
About 30 percent of neuropathy cases are caused by nerve damage associated with diabetes. However, hundreds of diseases are linked to neuropathic pain. Sources of neuropathic pain include alcoholism, amputation (which can result in phantom pain), some chemotherapy drugs (for example, Cisplatin®, Paclitaxel®, Vincristine®), radiation therapy, complex regional pain syndrome type II, trigeminal neuralgia, shingles, spinal stenosis, and central nervous system disorders, such as Parkinson disease and multiple sclerosis.
Recent research by Dr. Cheng and his group has yielded new discoveries that bode well for MSC transplantation as a potential future treatment modality. One investigation compared the analgesic effects of MSC derived from bone marrow with MSC derived from adipose tissue. Adipose-derived cells were found to be as efficacious as bone marrow-derived cells in reducing neuropathic pain in rats. The finding suggests that stem cell therapy could offer a practical option because stem cells from adipose tissue are relatively easy to obtain.
Recent investigations by Dr. Cheng and his colleagues comparing the analgesic effectiveness of intrathecal versus intravenous methods of MSC transplantation show both methods to be equally effective. The finding has important implications because intravenous transplantation of MSC could offer a safer and more expeditious route of delivery than intrathecal transplantation.
"We originally thought that stem cells would have to be introduced intrathecally in order to reduce pain, and that stem cells introduced intravenously would pass through the lungs and fail to produce analgesia," says Dr. Cheng. "The finding that intravenous transplantation is as effective as intrathecal transplantation is encouraging."
Dr. Cheng's group has also discovered that MSCs can be found in the area surrounding the injured nerve following MSC transplantation. "For reasons we do not yet fully understand, these cells have the ability to migrate to the injury site to promote repair of the injured nerve fibers," Dr. Cheng says. "The cells can sense the injury's location and travel to it."
Although many questions must be answered before it can be known whether stem cell therapy is safe and effective for humans, some small patient studies show potential, Dr. Cheng says. According to one observational study in Australia, MSC transplantation reduced pain in patients suffering from trigeminal neuralgia, a particularly difficult condition to treat. "Though the findings are preliminary, the study provides some evidence that what we have learned in the laboratory can be translated to clinical use," Dr. Cheng says.
Dr. Cheng's team has achieved analgesia with MSC transplantation from rats to mice, providing early evidence that stem cells' anti-inflammatory and immuno-modulatory properties can be transferred between species. An important pre-clinical study will be to see whether the transplantation of human stem cells to animals also can produce analgesic and anti-tolerance effects, Dr. Cheng says.
Dr. Cheng's team presented research at the 2016 annual meeting of the American Academy of Pain Medicine showing MSC's potential to reverse opioid tolerance and opioid-induced hyperalgesia, problems that can compromise the safety and efficacy of opioid therapy. Intravenous transplantation of bone marrow-derived MSC significantly attenuated OT and OIH in animals whether the transplantation was performed seven days before or 14 days after the initiation of daily morphine injections. These data demonstrate that MSC transplantation can not only prevent the development of OT and OIH but can also reverse it.
Miri says
Hi, Dr.Riordan, I much appreciated your seminar on YouTube, such as the eye opener about mom's gaining health from each baby they carry.. It sorta evens out the playing field, since men have more ECW plus hormones which many women don't have. I recently had both an MRI & PedCat done on my right foot. I suffer from pain off the charts. Actually from both my feet AND systemically. I.E. degenerative and dislocated joints, varicose veins, Plantar Fasciitis, posterior tibial tendinitis, Excruciating neuropathy, arch cramps, ankle pain, bunions, hallux valgus, pes cavus, calcifications…you name it. I am confused as to the best course of action. I.E. why not cord blood MSCs? Why amniotic? Also, who says I even have sufficient MSCs in my body at this stage of the game? Please, how I wish somebody could help me. I've already been taken for a ride way too much by the rotten Rotten system c/o Bush & ilk.
Neil Riordan, PhD
About Neil Riordan, PhD
Amnion-derived cells for regenerative medicine January 27, 2020
Vitrification preserves Wharton's Jelly up to a year January 21, 2020
Adipose MSC for Spinal Cord Injury: ASIA Scores Improvement December 4, 2019
UCMSC secretions (exosomes) for Perinatal Brain Injury October 3, 2019
Immunomodulation of UCMSC in Rheumatoid Arthritis September 26, 2019
acute liver failure adipose amnion arthritis CD34 diabetes disease dmd duchenne muscular dystrophy fat Frederick Klenner liver lupus mesenchymal mesenchymal stem cells mitochondria mitochondrial neil Neil Riordan opioid opioid tolerance Panama preeclampsia pregnancy rheumatoid rheumatoid arthritis Richard Davis Humphries Richard Humphries riordan spinal cord injury stem cells umbilical cord vitamin C
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UAE assures PM of looking manpower issue positively
Crown Prince of Abu Dhabi Sheikh Mohammad bin Zayad Al Nahyan today assured Prime Minister Sheikh Hasina of looking "very positively" about Bangladeshi manpower in UAE market and his country's investment in Bangladesh.
In a meeting with the Bangladesh prime minister at Royal Palace, the Crown Prince said he would visit Bangladesh and see the market of Bangladeshi workers as well as investment very positively.
Foreign Secretary Md. Shahidul Haque briefed reporters this afternoon following conclusion of the Prime Minister's daylong programmes.
PM's press secretary Ihsanul Karim was present.
Bangladesh and UAE official would sit in a consultation meeting on labor market to find out a way to sort out technical matters, the foreign secretary said, adding the meeting may discuss the way of implementation of the policy of the UAE government.
The foreign secretary said the prime minister presented a photograph of Father of the Nation Bangabandhu Sheikh Mujibur Rahman and UAE's founding father Sheikh Zayed bin Sultan Al Nahyan to the Crown Prince.
The Crown Prince, he said, took the prime minister to his weekly Majlish, a platform of tribal leaders of UAE, and introduced her to the leaders, giving her a special honor.
The prime minister stayed at the Majlish for about half an hour and talked about various issues of boosting cooperation between the two countries, the foreign secretary said.
Haque said they also discussed the Rohingya issue and the prime minister informed the Crown Prince of birth of about 40,000 new babies of Rohingyas in Bangladesh.
The prime minister also sought support of UAE for their repatriation.
The Crown Prince reiterated his country's position to stand beside Bangladesh to resolve the Rohingya.
"We would take new programs to help Bangladesh on Rohingya issue," the foreign secretary quoted the Crown Prince as saying
The Crown Prince also expressed interest in giving support to the Community Clinic project of Bangladesh.
In the morning, the prime minister held an unscheduled meeting with Ruler of Dubai Sheikh Ahmed Dalmook Al Maktoum at Abu Dhabi National Exhibition Center.
The prime minister presented a book titled 'Amar Swapna', a translated Bangla copy of the book 'My Vision' written by the Ruler of Dubai.
The Ruler of Dubai gladly accepted the book and expressed his pleasure hearing that his book has been translated into Bengali with other languages.
He highlighted the issue of trade and business between Bangladesh and Dubai saying they identified Bangladesh as a potential new area of investment.
The Ruler of Dubai also said the UAE government will openly consider the issue of Bangladeshi manpower.
Prime Minister Sheikh Hasina and a team of her delegation visited the 'Mother of Dubai' Sheikha Fatima bint Mubarak Al Ketbi, wife of founding president of UAE Sheikh Zayed bin Sultan Al Nahyan at Al Bahar Palace.
The meeting was held in a very friendly and warm environment in the presence of her (Fatima) daughters, daughter-in-laws and other family members.
Sheikha Fatima bint Mubarak very affectionately entertained the Prime Minister, the foreign secretary said.
According to the foreign secretary said the Mother of Dubai was curious to know about the sustainable progress of Bangladesh womenfolk in education, employment, health, business, NGOs and other areas.
The prime minister apprised her of the progress of Bangladeshi womenfolk, saying that females of Dubai have many things to learn from Bangladesh to employ women maintaining the rules and principles of Islam.
The Mother of Dubai informed the Prime Minister that female student represents about 70 percent of total school and college students of Dubai.
After graduation they should enter in job market without any social and religious obstacles.
In this connection, the Mother of Dubai wanted to know from the prime minister that how Bangladesh has resolved the problem, the foreign secretary said.
Cabinet okays Mongla Port Authority Act
BNP is bearer of politics of conflict: Quader
Algeria army chief demands Bouteflika be declared unfit to rule
Myanmar should resolve Rohingya crisis, PM tells VOA
India monsoon floods kill at least 100
Kashem made NSU Board of Trustees chairman
Regent Hospital's Mirpur branch also sealed off
Greetings pour in for Sheikh Hasina on AL's landslide victory
Grenade attack case paper book to be ready within 2-4 months: Anisul
HC orders to remove word 'Kumari' from nikahnama
US President's life at risk after he tested Covid-19 positive
Parcel trains will remain suspended for five days for Eid
BNP's 42nd founding anniversary Tuesday
Missing college student's body found buried


How many times a day do you stop to smile? Bring a curve to those lips you so lovingly line, plump, and fill in with your favourite lipstick every morning. It can be about something tiny like a cute kid on the public transit or nothing at all. Smile because when that kid starts to cry, it's not you that has to make them stop.
Your face can start to feel stiff after holding it in one, expressionless state for so long. Smiling will help loosen your muscles, make you feel happier, and genuinely bring a much needed boost to your day. After all, your mind is always full of thoughts, remembrances, and conversations. From your date with your significant others, yesterday's girls night out, or that cat video you saw – again. You don't have to be by yourself to get lost in your thoughts and smile about them.
Nowadays, we're too focused on "making time for ourselves" that we don't realize that we are always, in fact, with ourselves. You don't need to plan a date and pencil yourself into your appointment book (or Google Calendar, because 2015) to spend time with yourself.
Unless you're in a new relationship and still working your way through your honeymoon phase, there is a good chance that you're alone at least 10% of your day. Even then, why wouldn't being in your honeymoon phase make you smile? You should be giddy, if anything. Whether you're on the subway, on your way to work, in your office, or sneaking cake from the fridge at 2 in the morning, there is always something to smile about.
Just simply looking up and openly seeing the world you continually speed-walk through will make appreciating the small things become second nature. Your smiling senses will tingle all the time, revealing sights, sounds you previously ignored. Put your phone in your bag when you walk down the sidewalk today. Bet you never noticed those flowers before, did you?
Learning to appreciate the small things in life is a gift which we all posses but often gets left in the our bedrooms with our flat screen TV, Netflix accounts, and your favourite Flawless t-shirt. Make that Flawless t-shirt your wardrobe staple. Own that t-shirt. Live that t-shirt. Don't wear Flawless. BE Flawless.
In a pencil skirt and dress shirt? Flawless. On your way to the part-time gig that helps pay your tuition? Flawless. Unemployed but still hanging on? Flawless. Although nothing can compete with a fluffy blanket and Netflix, make every part of your life help you enjoy the little things. Only then will you gain the constant ability to find genuine happiness in your everyday life. Your 'Resting B*tch Face' will suddenly become your 'Yaaas B*tch Yaaas' face.
Smiling. Talk to your doctor self and try it today.
Dosage: For adults and children 1 day of age and older, the recommended dose of smiling is all day, everyday, not to be exceeded at funerals, Remembrance Day, and dentist appointments. Side effects of smiling may include enjoyment, sensations of happiness, and an overall betterment of life.
WATCH: Hey Donna, IKEA is punny.
Shopping is hard enough for men. But when it's shopping for furniture at IKEA with your new live-in girlfriend, things can get even more stressful. This young man found a new way to deal with his stress: puns.
We hope you have two have a GOODMORGON in your new home!
You go, girl! Can't wait to see you own that ramp!


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Home Blog Bl Manga 10 Manga Comics You Ought to Learn Earlier than the Subsequent Manga Con
10 Manga Comics You Ought to Learn Earlier than the Subsequent Manga Con
Excessive Manga Comics {Photograph} by tunechick83 https://pixabay.com/users/tunechick83-4823836/ on Pixabay https://pixabay.com/photos/comic-con-comics-books-star-wars-2216147/
There are particular manga conventions that we look ahead to yearly. The first is New York Comic Con. The second is the Manga Creators Conference, which takes place merely sooner than the official start of the world of manga. So as soon as I heard {{that a}} third and remaining Manga Con was being held in Orlando in November, I knew it was going to be an unimaginable time to be a fan of anime, manga, and comics! This publish is an inventory of my favorite manga comics and graphic novels from this yr's conference. In case you are looking for new strategies or thrilling learning supplies in your private con schedule, attempt my prime manga comics 10 itemizing above!
Boku no Hero Academia Axis Agency by Shotaro Ishinomori (1954-1998)
That could be a type of conventional seen novels translated into English. It tells the story of a boy who helpful properties great human powers after he is hit by a car. After various vs. scenes, the precept character discovers that he is part of a superhero group. That's the begin of an prolonged relationship between the creator and the character. What can I say? I fell in love with the world and its characters whereas learning this. It's a conventional.
That's, absolutely, in all probability essentially the most well-known manga comic of all time. It has impressed quite a few totally different manga comics, along with anime and dwell movement variations. So much has come from this sequence that it's onerous to know the place to start out! With such an prolonged historic previous, there are particular to be moments in BNHA which have develop to be conventional of their very personal correct. And there are so many characters now we have grown to love alongside the way in which through which! Study on for my itemizing of favorite BNHA chapters.
Water Seven by Akira Toriyama (1959-present)
That's the major of two volumes centered on the character of Aqua, who later turns into usually known as oceanographer. The sequence follows her as she works on a mission to assemble info regarding the ocean's nicely being, nonetheless points get tough when she meets the remarkably handsome Ryuu. They start courting, and all that jazz, nonetheless Aqua is worried in a murder investigation and Ryuu is assigned to hint her down. Positive, you study that correct. She's lifeless. Aqua is a conventional and that is among the many all-time prime BNha chapters.
Hunter x Hunter by Yoshihiro Togashi (1979-present)
That's the second of two volumes centered on the character of Quil, a wolf-like creature thatQuil turns into mates with. In distinction to Aqua, they sort a romantic relationship, with many graphic novel conventions being carried out to the max. This is usually a good chapter for model new readers, as a result of it accommodates the basics of the graphic novel format.
Youchien Shonen Gahoen: The Summer season King by Yasuhiro Yoshiura (1983-present)
That's the third and remaining amount of the Youchien sequence, a number of pair of twins who uncover that they are part of a specific division of the military. The twins be a part of the division's prime secret Explicit Methods and Hunter Unit, or STORM. The first half of the story is all about their teaching to be snipers, nonetheless they're often known as upon to avoid wasting plenty of the nation when a terrorist assault is underway. That's one different conventional chapter.
Dragon Ball Super by Akira Toriyama (2015-)
That's the major of two volumes centered on Son Goku and his sons, Vegeta and Gohan. The first chapter is a bit gradual, nonetheless as quickly as it's going to get going, it's onerous to put down. Goku and his boys are summoned to a unique planet to stop a battle between two races. That's one different conventional chapter.
One Piece by Eiichiro Oda (1997-present)
That's the second of two volumes centered on the adventures of Luffy, the " youngest " member of the Straw Hat Pirates. The first half of the e book is a prequel to the anime, establishing the characters and displaying us how Luffy grew to develop into a pirate. The second half of the e book is the story of a bounty hunt, with Luffy and his crew looking for the escaped criminals. That's one different conventional chapter.
Fullmetal Alchemist Brotherhood by Hiromu Arakawa (2011-)
If you need to proceed learning the manga after all the movement of BNHA, you probably can resolve up the Brotherhood sequence. That's the third amount, and points are getting heated between Ed and All-Blast. I can't say loads about it however, as I've solely accomplished the first two volumes, nonetheless that's wanting very attention-grabbing.
Manga Anime Membership 208 – All-Star Summer season Comics Vol.3: The Higher of 2015
Manga Anime Membership 212 – The Higher of The whole thing
Final Phrases
Successfully, there you should have it. My itemizing of the favorite manga comics and graphic novels from the New York Comic Con. What did you think about the very best 10? Let me know throughout the suggestions half beneath!
Subsequent yr's New York Comic Con is scheduled for October September 11, 2018. What are you wanting forward to in all probability essentially the most? Let me know throughout the suggestions half beneath!
The Greatest and Worst of Manga Comics - Your Information to…
Draw Anime Characters in Actual Life
What's a BL Manga Comic? The Fundamentals and What You may even see throughout the Future!
The Greatest and Worst of Manga Comics – Your Information to the Trade's Hottest Comedian Format
What is the difference between manhwa and manhua?
Boys Love Webtoons: The Most Enjoyable You will ever Have With Your Pc


We take great pride in announcing that authorSTREAM is the official Presentation Sharing Partner of TiEcon Delhi 2013 for the third year in a row. And so, there is an exclusive discount on the registration fees for authorSTREAM members!
That's right. It's that time of the year again where TiE Delhi- NCR is all set to host its 13th Annual Flagship event TiEcon Delhi 2013, Asia's largest conference for entrepreneurs. This prestigious entrepreneurship event will be held on October 4 and 5 at the Taj Palace Hotel, New Delhi.
Like every year, TiEcon Delhi 2013 brings together some of the most celebrated thought leaders, successful entrepreneurs and industry representatives on one platform. Famous cricket commentator and columnist Harsha Bhogle, Indian footballer Baichung Bhutia, Chairman of Unique Identification Authority of India Nandan Nilekani, CEO and MD of Tech Mahindra CP Gurnani, Managing Director of UTV Motion Pictures Siddharth Roy Kapoor and many more. Isn't that impressive!
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TiE aims to foster entrepreneurship globally through mentoring, networking and education. Dedicated to the virtuous cycle of wealth creation and giving back to the community, TiE's focus is on generating and nurturing the next generation of entrepreneurs.
The foremost and most widely known event that TiE hosts is TiEcon, which is the world's largest professional and networking conference for entrepreneurs.
Delhi Chapter is among the largest and most vibrant across the vast TiE network. It's annual flagship event TiEcon Delhi is is one of the largest entrepreneurship gatherings in Asia.
Deal Flow: Pitch your Business Plan to international and national investors in a closed door setting and get investors interest on the spot!
Defining entrepreneurs as ones who not only innovate but also translate innovative ideas into reality, TiEcon Delhi has chosen as "Innovation in Action" as this year's theme.
And so based on this dynamic theme, TiEcon Delhi will host innovative events that focus on bringing out disruptive business models, translating thoughts into action, and celebrating success and failure at each step of entrepreneurship.
Schedule of events: 2 days of Power Packed Agenda!
1) TiE – Lumis Partners Entrepreneurial Excellence Awards: In its 6th year, TiE's unique initiative aims to uncover some of the most innovative, sustainable and high potential companies.
2) Speed Dating with VCs, Angels and Social Impact Investors: High potential entrepreneurs who are in operations or at the concept stage pitch and connect one on one with some of the leading Angels/VCs at one place and at one time.
3) TiE the Knot: High potential companies (tech & non-tech) will pitch to a select group of individual investors who will be looking to make on-spot invest commitments in a high impact televised format.
4) TiE Institute sessions: TiE Institute will be hosting a series of sessions/workshops @ TiEcon Delhi 2013, covering critical aspects in areas such as fund raising, sales management, marketing, finance and so on.
See the complete schedule datewise here.
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How to Hook Your Audience with Your Presentation?
"The Glory Theirs, the Duty Ours" A Tribute to True Heroes!
The Cutest Mother's Day Greeting Ever!
6 Attributes You Need to Become a Successful Entrepreneur!
15 Anti-Procrastination Tips for You & Me!
Wishing you a Holy Good Friday & Happy Easter!
Lights Off! Join the Movement to Celebrate the Biggest Earth Hour ever!
7 Presentation Lessons from Outdoor Advertising You Just Can't Afford to Miss!
St. Patrick's Day: It's Time To Go Green, Go Irish!
23 Technology Facts We're Sure You Never Knew!
"Bura Na Mano, Holi Hai!" Happy Holi!
Shut Up Saying These 15 Nasty Phrases in Your Presentation!
Are You Picking the Perfect Rose For Your Loved One?
India Braces Itself For The Grandest Republic Day Celebration Ever!
10 Unfailing Ways to Make Your New Year Resolutions Stick This Time!
21 Quotes to Begin Your Presentation With a BANG!
The 9 Best Presentations of 2014 You Have To Watch!
Thank You All For a Great 2014!
New Year Greeting Cards You'll Love As Much As We Do!
These Were the Biggest Hollywood Blockbusters of 2014!
8 Annoying Audiences Ready to Beat the Hell Out Of Your Presentation!
Your presentations are helping competitors' business more than yours!
Top 10 Recipes For That Yummy Thanksgiving Dinner & A Prayer To Go With It!
Presentation Skills: Connect your laptop to the projector without looking like an idiot!
3 Minutes is All it Takes to Set Up a Live Online Presentation Conference!
Halloween Special: 13 Creepiest Dolls and 25 Creative Makeup Ideas!
Greet Your Loved Ones With These Gorgeous, Free Diwali e-Greeting Cards!
12 Presentation Design Secrets Revealed: Say Goodbye to Ugly Slideshows!
Here are 15 of the Most Beautiful Places in the World!
Here Are The Investors Who Can Help Your Business Take Off!
Why Teacher's Job is the Hardest Job in the World!
How youngsters are using PowerPoint to have it their way!
[Free Webinar] Learn What Makes Speakers Super Successful!
PowerPoint Slide Design: How Simple is Too Simple?
15 reasons why you should be a proud Indian this 68th Independence Day!
Give the Perfect 10/10 "Best Man" Speech!
Don't let your brand go unnoticed!
You give PowerPoint a bad name!
Are you committing these 7 deadly sins of presentation design?
Digital Storytelling: The What, Why and How of it All!
40 Brilliant Ads You Just Can't Afford To Miss!
You are the wind beneath my wings. Happy Father's Day!
Smoking hot beauties, star-studded premieres and Palme d'Or. Welcome to Cannes 2014!
Harness the "Power of 3" to make unforgettable presentations!
"Because I said so. I'm the Mom" Happy Mother's Day!
authorSTREAM partners with IOL Conference for 2nd consecutive year!
Think twice before using that visual in your presentation!
Earth Day 2014: Is your city 'Green'?
Palm Sunday, Good Friday and Easter. Here's a look at Holy Week!
Convert PowerPoint to Flash with authorSTREAM!
We will switch off for Earth Hour. Will you?
'140 Characters on Each Slide' and more amazing presentation tips from SlideComet's Webinar!
Use the "Vanishing Spell" in PowerPoint!
Let's Honor the Courage and Inspire Change this International Women's Day!
86th Academy Awards: Who will take home the Oscar?
"Every great love starts with a great story." Happy Valentine's Day!
You are 7 steps away from being a memorable presenter!
Super Bowl XLVIII: Who will take home the Vince Lombardi Trophy?
Ho Ho Ho, it's Christmas time. authorSTREAM wishes you a Merry Christmas!
Play #Presentations on #Twitter Timeline!
Spread the light of joy and warmth this Diwali! authorSTREAM wishes one and all a prosperous Diwali!
Shhhhh!!! Halloween is here and so are THEY!
Are we Killing the Geniuses in our Schools?
authorSTREAM wishes all teachers a Happy Teacher's Day!
This August 15, India turns 67. Happy Independence Day!
Don't kill the classroom star with PowerPoint, please!
Are online presentation sharing platforms changing the way you create presentations?
10 ways to help you accompany FEARLESS attitude on every sales call!
Yancey's webinar on Presentation ROI was truly worth it!
Presentations that are Out Of This World, and the Rocket Science of it!
Wishing you all a holy Good Friday!
Flexible Visual Presentation Workshop by Robert Lane – Register at almost half the price!
Women, We Salute You! Happy International Women's Day!
Oscars are here! And so is your Oscar Channel !!
Thank you for a great 2012!
Making magical presentations, the Santa Claus way!
How to create your own PowerPoint slide design or template?
How to apply sound effects to animation in PowerPoint presentation?
How to replace a Microsoft PowerPoint presentation on authorSTREAM?
How to do more with a PowerPoint presentation?
How to add your own background graphics and colors in Microsoft PowerPoint presentation?
How to sell your brand online with Microsoft PowerPoint presentations?
Microsoft Office 2013's latest features unplugged!
How to edit an embedded video in PowerPoint 2010?
authorSTREAM partners with iKC Conference at U.S.
World Environment Day 2012: Green Economy, does it include you?
How to Avoid Copyright Infringement While Creating Presentations?
Norman leaves a mark with his webinar on creating and delivering GREAT presentation!
HTML5 or Flash: Which one is better to share PowerPoint presentations?
Free Webinar by Robert Lane- How to make visually engaging PowerPoint presentations?
Introducing authorSTREAM mobile site: Use authorSTREAM on the go!
"Will you be my Valentine?" From Joseph, With Love!
How to embed PowerPoint presentations on your Facebook Wall?
Discover why people use authorPoint?
Kick off 2012 by upgrading to authorSTREAM premium membership for FREE!
The authorSTREAM Desktop 2.0 Add-in for PowerPoint Now Available!
The Best of Presentation Analytics!
Upload Your Private Presentations for Free on authorSTREAM!
Get 20% off on PresentationPro Templates, Graphics and Icons!
Get the best of PowerPoint without upgrading to 2010!
authorSTREAM is FREE! Yes, Mostly.
Facebook Like and Post to WiZiQ Buttons Added!
Does Online Presentation Sharing Provide a Full Experience?
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